Nicholas H. Barton

What determines the genetic contribution that an individual makes to future generations? With biparental reproduction, each individual leaves a “pedigree” of descendants, determined by the biparental relationships in the population. The pedigree of an individual constrains the lines of descent of each of its genes. An individual’s reproductive value is the expected number of copies of each of its genes that is passed on to distant generations conditional on its pedigree. For the simplest model of biparental reproduction (analogous to the Wright–Fisher model), an individual’s reproductive value is determined within ∼10 generations, independent of population size. Partial selfing and subdivision do not greatly slow this convergence. Our central result is that the probability that a gene will survive is proportional to the reproductive value of the individual that carries it and that, conditional on survival, after a few tens of generations, the distribution of the number of surviving copies is the same for all individuals, whatever their reproductive value. These results can be generalized to the joint distribution of surviving blocks of the ancestral genome. Selection on unlinked loci in the genetic background may greatly increase the variance in reproductive value, but the above results nevertheless still hold. The almost linear relationship between survival probability and reproductive value also holds for weakly favored alleles. Thus, the influence of the complex pedigree of descendants on an individual’s genetic contribution to the population can be summarized through a single number: its reproductive value.

Under the classical view, selection depends more or less directly on mutation: standing genetic variance is maintained by a balance between selection and mutation, and adaptation is fuelled by new favourable mutations. Recombination is favoured if it breaks negative associations among selected alleles, which interfere with adaptation. Such associations may be generated by negative epistasis, or by random drift (leading to the Hill–Robertson effect). Both deterministic and stochastic explanations depend primarily on the genomic mutation rate, U . This may be large enough to explain high recombination rates in some organisms, but seems unlikely to be so in general. Random drift is a more general source of negative linkage disequilibria, and can cause selection for recombination even in large populations, through the chance loss of new favourable mutations. The rate of species-wide substitutions is much too low to drive this mechanism, but local fluctuations in selection, combined with gene flow, may suffice. These arguments are illustrated by comparing the interaction between good and bad mutations at unlinked loci under the infinitesimal model.

Summary: Explicit formulae are given for the effects of a barrier to gene flow on random fluctuations in allele frequency; these formulae can also be seen as generating functions for the distribution of coalescence times. The formulae are derived using a continuous diffusion approximation, which is accurate over all but very small spatial scales. The continuous approximation is confirmed by comparison with the exact solution to the stepping stone model. In both one and two spatial dimensions, the variance of fluctuations in allele frequencies increases near the barrier; when the barrier is very strong, the variance doubles. However, the effect on fluctuations close to the barrier is much greater when the population is spread over two spatial dimensions than when it occupies a linear, one-dimensional habitat: barriers of strength comparable with the dispersal range (B≈σ) can have an appreciable effect in two dimensions, whereas only barriers with strength comparable with the characteristic scale ( B\! \approx\! L \equals \sigma \sol \sqrt {2 \mu}\hskip2 ) are significant in one dimension (μ is the rate of mutation or long-range dispersal). Thus, in a two-dimensional population, barriers to gene flow can be detected through their effect on the spatial pattern of genetic marker alleles.

Evolution at multiple gene positions is complicated. Direct selection on one gene disturbs the evolutionary dynamics of associated genes. Recent years have seen the development of a multilocus methodology for modeling evolution at arbitrary numbers of gene positions with arbitrary dominance and epistatic relations, mode of inheritance, genetic linkage, and recombination. We show that the approach is conceptually analogous to social evolutionary methodology, which focuses on selection acting on associated individuals. In doing so, we (1) make explicit the links between the multilocus methodology and the foundations of social evolution theory, namely, Price’s theorem and Hamilton’s rule; (2) relate the multilocus approach to levels‐of‐selection and neighbor‐modulated‐fitness approaches in social evolution; (3) highlight the equivalence between genetical hitchhiking and kin selection; (4) demonstrate that the multilocus methodology allows for social evolutionary analyses involving coevolution of multiple traits and genetical associations between nonrelatives, including individuals of different species; (5) show that this methodology helps solve problems of dynamic sufficiency in social evolution theory; (6) form links between invasion criteria in multilocus systems and Hamilton’s rule of kin selection; (7) illustrate the generality and exactness of Hamilton’s rule, which has previously been described as an approximate, heuristic result.

The extent of genetic variation in fitness is a crucial issue in evolutionary biology and yet remains largely unresolved. In Drosophila melanogaster, we have devised a method that allows the net effects on fitness of heterozygous wild-type chromosomes to be measured, by competing them against two different “balancer” chromosomes. We have applied the method to a large sample of 40 wild-type third chromosomes and have measured fitnesses of nonlethal chromosomes as well as chromosomes bearing recessive lethals. The measurements were made in the environment to which the population was adapted and did not involve inbreeding. The results show an extraordinary similarity in the behavior of replicates of the same chromosome, indicating consistent genetic effects on total fitness. Some invading chromosomes increased rapidly and some slowly, and some rose to appreciable frequency after several months, but then declined again: in every case, the same pattern was seen in each replicate. We estimated relative fitnesses, rates of change of fitness, and relative viabilities, for each chromosome. There were significant fluctuations around the fitted model, which were also highly replicable. Wild-type chromosomes varied substantially in their effects on heterozygous fitness, and these effects vary through time, most likely as a result of genotype × environment interactions.